Re: st: Chow test to test only slope coefficient and importance of dummy variable?

[Sarah Vinette <savinett@ucalgary.ca>]

Thank you very much for your explanations David, they are very helpful.

On 2013-11-14, at 12:52 PM, David Hoaglin wrote:

> Hi, Sarah.
> 
> Your tests look all right to me, except for the last one.  If the two
> groups have different slopes, it may not be meaningful to test whether
> they have the same intercept.  A possible exception is a model in
> which the predictor variable is centered (at the same value across the
> groups); one might be interested in whether the data are compatible
> with lines for the two groups that pass through the same point at that
> value of the predictor, but I don't have an actual example in mind.
> 
> I would describe the actual tests and not mention "Chow Test."
> 
> David Hoaglin
> 
> On Thu, Nov 14, 2013 at 2:30 PM,  <savinett@ucalgary.ca> wrote:
>> Thank you very much for your informative and helpful responses Fernando
>> and David, I really appreciate it.  I think I understand, I just want to
>> confirm my understanding and that I am doing this properly. For my study,
>> I only have 1 independent variable (I will call this mpg to be consistent
>> with the FAQ example).
>> 
>> From what I understand, even if I am only interested in the difference in
>> slopes, I use a model that allows the groups to differ in both slopes and
>> intercepts. So I will include group2 in the regression to allow the groups
>> to have different intercepts and use the command:
>> . regress price mpg mpg2 group2
>> 
>> Then, if I wish to only test a difference in slopes, I would follow this
>> up with:
>> . test _b[mpg2]=0
>> 
>> If I wanted to test both the intercept and slope I would use:
>> . test _b[mpg2]=0, notest
>> . test _b[group2]=0, accum
>> 
>> and if I were only interested in if the groups differed by intercept I
>> would use:
>> . test _b[group2]=0
>> 
>> If you would please let me know if this is correct that would be awesome.
>> 
>> Also, David, you had mentioned in your response that it is best not to
>> focus on the Chow Test specifically. I am wondering for my description of
>> the statistical approach is it correct to describe it as a Chow Test where
>> only differences in slope were assessed? Or would it be better to instead
>> describe the steps taken (and not label it with the words Chow Test)?
>> Thank you very much again for your time and guidance!
>> 
>> Sarah
>> 
>>> Hi, Sarah.
>>> 
>>> As that FAQ explains, we would do well not to focus so firmly on the
>>> "Chow Test."  Greg Chow's 1960 result was helpful years ago, but
>>> software has given us the flexibility to do that test and much more.
>>> For many statisticians, hiding a straightforward test behind the name
>>> "Chow Test" will produce puzzled looks.
>>> 
>>> You can test whether only the slopes are different and allow each
>>> group to have its own intercept.  In fact, that is the usual situation
>>> (e.g., a one-way analysis of covariance fits a common slope and
>>> separate intercepts).  As in the example in that FAQ, you can fit the
>>> model that has separate intercepts and separate slopes and then test
>>> whether the slopes are equal.
>>> 
>>> That example did not use "noconstant" to remove the intercept from the
>>> model.  It used that option in order to use separate coefficients
>>> (including the constant) for each group.  In the command
>>> . regress price mpg weight mpg2 weight2 group2
>>> _const is the intercept for Group 1, and _const + _b[group2] is the
>>> intercept for Group 2.  Also, the coefficient of mpg for Group 2 is
>>> _b[mpg] + _b[mpg2], so the test of whether the coefficients of mpg in
>>> the two groups are equal is the test of whether _b[mpg2] = 0.  (I am
>>> assuming that mpg2 equals the product of mpg and the Group 2
>>> indicator.)
>>> 
>>> David Hoaglin
>>> 
>>> Chow GC (1960).  Tests of equality between sets of coefficients in two
>>> linear regressions.  Econometrica 28:591-605.
>>> 
>>> On Wed, Nov 13, 2013 at 4:35 PM,  <savinett@ucalgary.ca> wrote:
>>>> Hi,
>>>> 
>>>> I am new to Stata and the Chow Test. I want to compare the slopes of
>>>> two
>>>> sets of time series data using the chow test, however I am not
>>>> interested
>>>> in any differences in the intercepts of these time series data.  I have
>>>> read the FAQs section on this and found this one:
>>>> http://www.stata.com/support/faqs/statistics/chow-tests/ to be very
>>>> helpful.  I do, however, have two questions:
>>>> 
>>>> 1.   Can I use the Chow Test to test that only the slopes are different
>>>> (not both the slope and intercepts)? I still want to include the
>>>> intercept
>>>> in the model (i.e. not use the “noconstant”). However, for the Chow
>>>> Test I
>>>> would like it to reflect that if there is a significant difference
>>>> between
>>>> the groups that this is due to a difference in their slopes (as I
>>>> expect
>>>> that their intercepts will differ and am not interested this aspect).
>>>> 
>>>> 2.  It is not clear to me why the in the example from the Chow Test FAQ
>>>> (link in the first paragraph) “group2” (the dummy variable) is
>>>> included in
>>>> the regression:
>>>> . regress price mpg weight mpg2 weight2 group2
>>>> 
>>>> If someone could please provide me with some insight that would be
>>>> amazing.
>>>> Thank you very much in advance for your help with my questions!
>>>> 
>>>> Sarah
>>> 
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>>> 
>> 
>> 
>> 
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